Ükenbreker

Explanation of the quadratic formula:

"In elementary algebra, the quadratic formula is a formula that provides the
solution(s) to a quadratic equation.
There are other ways of solving a quadratic equation instead of using the quadratic formula,
such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others.

Given a general quadratic equation of the form
ax^2+bx+c=0.

with x representing an unknown, a, b and c representing constants with a ≠ 0, the quadratic formula is:
x = [-b ± √(b^2 - 4ac)]/2a

Each of these two solutions is also called a root (or zero) of the quadratic equation.
Geometrically, these roots represent the x-values at which any parabola,
explicitly given as y = ax2 + bx + c, crosses the x-axis.
As well as being a formula that yields the zeros of any parabola,
the quadratic formula can also be used to identify the axis of symmetry of the parabola,
and the number of real zeros the quadratic equation contains."
-Wikipedia

Derivation Using 'Completing the Square':

Proof:
(ax^2)+bx+c=0, where (a≠0)

(x^2)+(b/a)x+(c/a)=0

(x^2)+(b/a)x=(-c/a)

(x^2)+(b/a)x+[(b^2)/4(a^2)]=(−c/a)+[(b^2)/4(a^2)]

(x+b2a)^2=[(b^2)−(4ac)]/(4a^2)

[(x)+(b/2a)]=±[√(b^2)−(4ac)]/[√(4a^2)]

Therefore, x = [-b ± √(b^2 - 4ac)]/2a
                                                                   QED